A nonlinear and dispersive APML ABC for the FD-TD methods

We have developed a modified anisotropic perfectly matched layer (APML) absorbing boundary condition (ABC) for the finite-difference time-domain (FD-TD) analysis of nonlinear and dispersive media. The formulation is a simple modification to the original nonsplit APML, and retains the robustness and the simple implementation in the FD-TD and the higher-order schemes. The proposed ABC has a broad area of application, and is especially suitable for the analysis of nonlinear optical waveguide problems.     

等离子体散射FDTD分析的移位算子方法

色散介质的介电系数是频率的函数，使本构关系在时域成为卷积关系，这就给应用FDTD方法计算色散介质中波的散射和传播带来困难。文中把色散介质的相对介电系数写成以jω为自变量的有理分式函数，用δ/δt代替jω，过渡到时域，再引入离散时域移位算子代替时间微分算子来处理有理分式函数形式的介电系数，进而导出FDTD中电位移矢量D和电场强度E之间的关系。所得结果与Z变换理论的梯形近似结果一致，但与Z变换理论相比较，移位算子方法推导简单，概念简明。文中用移位算子结合FDTD方法分别计算一维等离子体平板的反射系数和二维等离子体柱的远场散射。所得结果与用Z变换理论结合FDTD方法计算的结果相符合。     

Parameterization of media dispersive properties for FDTD

Convenient means of obtaining a Debye model of the dielectric dispersion are given for media whose properties are given either by the Cole-Cole model or numerical data in the frequency domain     

High-order FDTD and auxiliary differential equation formulation of optical pulse propagation in 2-D Kerr and Raman nonlinear dispersive media

We reformulate the existing auxiliary differential equation (ADE) technique in the context of the finite-difference time-domain analysis of Maxwell's equations for the modeling of optical pulse propagation in linear Lorentz and nonlinear Kerr and Raman media. Our formulation is based on the polarization terms and allows simple and consistent implementation of such media together with the anisotropic perfectly matched layer (APML) absorbing boundary condition. The disadvantages of the ADE technique, i.e., requiring additional storage for auxiliary variables, has been overcome by adopting the high-order finite-difference schemes derived from the previously reported wavelet-based formulation. With those techniques, we demonstrate in two-dimensional setting an effective and accurate numerical analysis of the spatio-temporal soliton propagation as a consequence of the physically originated balanced phenomena between the self-focusing effect of nonlinearity and the pulse broadening effects of the temporal dispersion and of the spatial diffraction.     

A novel FDTD formulation for dispersive media

A novel FDTD formulation for dispersive media called piecewise linear JE recursive convolution (PLJERC) finite-different time-domain (FDTD) method is derived using the piecewise linear approximation and the recursive convolution relationship between the current density J and the electric field E. The high accuracy and efficiency of the PLJERC method is confirmed by computing the reflection coefficients of an electromagnetic wave through a collision plasma slab in one dimension.     

Small signal analysis for dispersive optical fiber communicationsystems

A small signal analysis for analyzing the conversion between intensity and phase modulation or noise in a dispersive fiber is given. Using this theory the small signal response of laser diodes with respect to intensity and phase modulation in dispersive optical fibers is derived. Guidelines are also given for considerably reducing the intensity noise if a fiber with a suitable dispersion is used. All analytical calculations are compared with numerical simulations and good agreement is achieved     

分布式PT对称非线性耦合器中光纤孤子间的相互作用

为了在光纤孤子的应用装置中讨论孤子稳定性和相互作用,数值地研究了变系数耦合非线性薛定谔方程组。结果发现微孤子相互作用存在于具有周期分布的色散和非线性参量的PT对称非线性耦合器中。而且,在不同初始条件下,包括同相输入的两个或三个等幅孤子,及含反相二孤子输入的三孤子,都存在这样的微孤子相互作用。此外,还讨论了在有限初始扰动下微孤子相互作用的稳定性。结果表明,有限初始扰动不会影响微孤子相互作用的主要特征。     

N阶色散媒质的FDTD法与数字信号处理技术

提出了一种新的N阶色散媒质的时域分析方法,并将其表征为一组无限冲击响应滤波器,将色散媒质在FDTD中的表述问题转化为数字滤波器(IIR)的设计问题.改进FDTD能分析处理与频率有关的电磁场问题.为验证此方法的有效性和可靠性,用此方法计算了高斯平面波脉冲入射N阶色散媒质的情况,计算结果与解析值非常吻合.     

Stable droplets and dark-ring cavity solitons in nonlinear optical devices

Two kinds of cavity solitons, stable circular domain walls (droplets) and dark-ring cavity solitons, are presented in models of vectorial Kerr resonators and degenerate optical parametric oscillators. These structures are universal in systems with two equivalent homogeneous states and are found for parameter values close to those of a modulational instability of a flat front. Stable droplets owe their existence to curvature effects and, therefore, they are not present in one-dimensional systems. We show that stable droplets nucleate out of dark-ring cavity solitons and that in some systems there are regimes in which they coexist.     

Twofold Mur's first-order ABC in the FDTD method

In this paper, it is shown that the reflection error of Mur's first-order absorbing boundary condition (ABC) can be canceled effectively by applying the ABC twice to an electromagnetic (EM) field on two diagonally neighboring nodes on the x-t, y-t and t-t planes. Following this idea, we have developed a twofold Mur's first-order ABC (TMFABC), which is efficient to absorb both propagative and evanescent EM waves and very convenient for implementation to multilayered structures. TMFABC improves Mur's first-order ABC more effectively at lower frequencies. This is very important because most energy of a high-speed pulse is concentrated at lower frequencies     

FDTD analysis of nonlinear magnetic diffusion by reduced c

The finite-difference time-domain (FDTD) approach is a particularly useful method for investigating nonlinear electromagnetics because the nonlinear relationships may be directly incorporated into the equation for advancing the electromagnetic fields. This approach is applicable to nonlinear magnetic materials with or without hysteresis (i.e. time dependence). Problems with geometric details that are very small compared to signal wavelengths, however, stress FDTD techniques. This occurs because the Courant-limited Δt can become small enough to require the use of >10¹¹ time steps unless one is tricky. Tricky means observing that this sort of problem has a solution which seldom depends on the speed of light c. Here, we demonstrate a procedure to elude the Courant stability condition by defining c to be 100 m/s. The present problem arose out of a magnetic diffusion FDTD application. The “reduced-c” technique should work, however, for any problem where Δt is limited by Δx/c which, in turn, is limited by the smallness of the problem geometry, not by a need for extremely fine temporal electromagnetic resolution     

An FDTD formulation for dispersive media using a current density

A novel finite-difference time-domain (FDTD) formulation for dispersive media called the JE convolution (JEC) method is derived using the convolution relationship between the current density J and the electric field E. The high accuracy of the JEC method is confirmed by computing the reflection and transmission coefficients for a nonmagnetized plasma slab in one dimension. It is found that the new method has an accuracy comparable to the auxiliary differential equation (ADE) while having the same computational efficiency as the less accurate recursive convolution (RC) method. Numerical simulations also show that the JEC method exhibits significantly higher accuracy than the RC method in modeling wave attenuation inside the plasma     

Subcell FDTD modeling of electrically thin dispersive layers

A novel technique for treating electrically thin dispersive layers with the finite-difference time-domain (FDTD) method is introduced. The proposed model is based on the subcell technique, where the constitutive relations are locally averaged in the FDTD grid. The most significant feature of the proposed model is its ability to model rather complicated dispersive layers having multiple pole pairs. The model is validated with several numerical examples making comparison with the exact results. Both time- and frequency-domain validations are presented.     

Effective permittivity at the interface of dispersive dielectrics in FDTD

A simple treatment of E-field component tangential to dispersive media interfaces in FDTD is introduced. The method uses concepts from the auxiliary differential equations method to average the constitutive parameters. The cases of a wave propagating in a coaxial line and of an open-ended coaxial line radiating into the dispersive media are investigated. Results show that the simulations could be significantly erroneous if the interface is not handled properly.     

Nonlinear codes for dispersive nonlinear fibers

We consider a single wavelength channel in a nonlinear dispersive single-mode fiber. We simulate the propagation of binary sequences using on-off keying return-to-zero modulation at a bit rate of 10 Gb/s, under different dispersion and input power conditions. We determine the impact that dispersion and nonlinearity have on the pulse sequences by measuring the Euclidian distances (EDs) among all pairs of received sequences. We then model the set of EDs as a fully connected graph and by means of a clique-finding algorithm we search for subsets of sequences that form codes matched to this nonlinear channel, resulting in significant bit-error-rate improvement.     

FDTD analysis of wave propagation in nonlinear absorbing and gainmedia

An explicit finite-difference time-domain (FDTD) scheme for wave propagation in certain kinds of nonlinear media such as saturable absorbers and gain layers in lasers is proposed here. This scheme is an extension of the auxiliary differential equation FDTD approach and incorporates rate equations that govern the time-domain dynamics of the atomic populations in the medium. For small signal intensities and slowly varying pulses, this method gives the same results as frequency-domain methods using the linear susceptibility function. Population dynamics for large signal intensities and the transient response for rapidly varying pulses in two-level (absorber) and four-level (gain) atomic media are calculated to demonstrate the advantages of this approach     

Optimization of subgridding schemes for FDTD

A procedure to optimize the coupling coefficients between fine and coarse mesh regions for two-dimensional (2-D) finite-difference time-domain (FDTD) subgridding algorithms is introduced. The coefficients are optimized with respect to different angles and expanded in a form suitable for FDTD computation     

Small signal analysis with higher-order dispersion for dispersive optical communication systems

In this paper an improved small-signal analysis has been presented for analyzing the influence of the higher-order dispersion terms on dispersive optical communication systems operating near zero-dispersion wavelength for single mode fiber. A generalized conversion matrix has been reported that gives the transfer function of intensity and phase from the fiber input to fiber output for laser source including the influence of any higher-order dispersion term. In addition, analysis is applicable to evaluate the impact of combined or independent dispersion terms on small-signal frequency response and relative intensity noise (RIN) response of an ultrafast laser diode including noises due to laser spontaneous emission rate and average photon density. These responses are plotted for second-, third-, and fourth-order dispersion terms and their combinations. It is observed that the higher-order dispersion terms have significant impact on frequency and RIN responses at large modulating frequencies and large propagation distances.     

Accuracy improved multi-stage ADI-PML algorithm for dispersive open region FDTD problems

An unconditionally stable multi-stage alternating direction implicit perfectly matched layer (ADI-PML) algorithm is presented for modelling dispersive open region finite difference time domain (FDTD) applications. In the proposed algorithm, the updating procedure of the field equations from the nth to (n t 1)th time step is carried out in four stages with a time increment of Dt/4. Numerical examples carried out in two dimensions show that the proposed algorithm presents significant improvement over the conventional ADI-PML algorithm for different Courant-Friedrichs-Lewy numbers and for different cell sizes per wavelength.     

FDTD for Nth-order dispersive media

Previously, a method for applying the finite-difference time domain (FDTD) method to dispersive media with complex permittivity described by a function with a single first-order pole was presented. This method involved the recursive evaluation of a discrete convolution, and was therefore relatively efficient. In this work, the recursive convolution approach is extended to media with dispersions described by multiple second-order poles. The significant change from the first-order implementation is that the single backstore variable for each second-order pole is complex. The approach is demonstrated for a pulsed plane wave incident on a medium with a complex permittivity described by two second-order poles, and excellent agreement is obtained with the exact solution